Equation REF  and REF  is repeated for all \(k\)  node partitions. This stochastic sampling process assigns \(k\)  potential edge \(e_{i,j}\)  from vertex \(u_i\)  to \(u_j\)  for each vertex pair \((u_i, u_j)\) . We select the top-k edge connections such that the top-k node candidates are set to 1 while the rest of the node pairs are set as zero. The sampled edge weights computed correspond to discrete variables. In such a case, the edge weights in the Adaptive Graph Learning Layer cannot be updated vie backpropogation. In order to convert these weights into continuous probabilistic distribution, we employ the Gumbel-softmax reparametrization technique [1]}, as given by \(w_{i,j}= softmax((e_{i,j} + q)/\tau )\) , to enable gradients computation. Here, \(q\)  is a random vector whose components are independent and identically distributed and \(\tau \)  is the softmax temperature that controls sampling smoothness. The process outlined in the above steps helps to learn stable node relationships over the training period. The hyper parameters \(\omega \)  and \(\lambda \)  are adjusted over the course of gradient backpropogation as new training data updates the model.
